Can you run modern warfare 3 on a Toshiba satellite a505-s6025 with four gb of ram and an nvidia geforce 310m graphics card?

I don't think so, thats a pretty awful card.

Newest intel graphics are better.

But, you can upgrade it to a gt 230m which is a lot better.

Toshiba part number is V000190390. Make sure you get the right part, you'll also need some cooling paste.